An acoustic wave imaging apparatus (ultrasound wave imaging apparatus, in a case of using an ultrasound wave) which generates a three-dimensional structural image inside an object using an acoustic wave, such as an ultrasound wave, is widely used in medical fields as an inexpensive medical image diagnostic apparatus which produces few side effects. The performance of medical image diagnostic apparatuses improves every year due to improvements in acoustic wave imaging technology. As one technology which further improves performance, an image reconstruction technology using a CMP (Constrained Minimization of Power) method is under research.
The CMP method is a signal processing technology developed as an adaptive antenna technology. The CMP method is a reception method which adaptively adjusts the directivity of reception under a constraint such that the receive gain of a radio wave coming from a desired direction is kept constant, so as to constantly minimize the power of all the received signals, including any interfering waves. According to this method, signals with a good SN ratio can be received, since the ratio of power of any interfering waves to that of desired wave can be minimized.
Adaptive antenna technology is based on the assumption that an array antenna constituted by a plurality of receiving elements is used, and the concrete calculation of the CMP method is generally as follows.
It is assumed that the received signals of n number of receiving elements of an array antenna are x[k, t] (k=1, 2, . . . , n) in a complex signal form.
It is assumed that the weights of n of complex numbers are w[k] (k=1, 2, . . . , n).
In this case, the output s[t] of the array antenna can be given by Expression (1):
                    [                  Math          .                                          ⁢          1                ]                                                                      s          ⁡                      [            t            ]                          =                              ∑            k                    ⁢                                                    w                ⁡                                  [                  k                  ]                                            *                        ·                          x              ⁡                              [                                  k                  ,                  t                                ]                                                                        (        1        )            
Instantaneously received power p[t] is given by Expression (2), in which an asterisk (*) at the right shoulder of a variable identifies a complex conjugate:
                    [                  Math          .                                          ⁢          2                ]                                                                      p          ⁡                      [            t            ]                          =                              1            2                    ·                                                                                    ∑                  k                                ⁢                                                                            w                      ⁡                                              [                        k                        ]                                                              *                                    ·                                      x                    ⁡                                          [                                              k                        ,                        t                                            ]                                                                                                          2                                              (        2        )            
If the received power P used for the CMP method is defined as an integration value of the instantaneously received power p[t] within a predetermined time, the received power P is given by Expression (3) in vector form:
                    [                  Math          .                                          ⁢          3                ]                                                                                                P              =                            ⁢                                                ∑                  t                                ⁢                                  p                  ⁡                                      [                    t                    ]                                                                                                                          =                            ⁢                                                1                  2                                ·                                                      ∑                    t                                    ⁢                                                                                                                                    ∑                          k                                                ⁢                                                                                                            w                              ⁡                                                              [                                k                                ]                                                                                      *                                                    ·                                                      x                            ⁡                                                          [                                                              k                                ,                                t                                                            ]                                                                                                                                                                  2                                                                                                                          =                            ⁢                                                1                  2                                ·                                                      ∑                                          k                      ⁢                                                                                          ⁢                      1                                                        ⁢                                                            ∑                                              k                        ⁢                                                                                                  ⁢                        2                                                              ⁢                                          (                                                                                                    w                            ⁡                                                          [                                                              k                                ⁢                                                                                                                                  ⁢                                2                                                            ]                                                                                *                                                ·                                                  (                                                                                    ∑                              t                                                        ⁢                                                                                          x                                ⁡                                                                  [                                                                                                            k                                      ⁢                                                                                                                                                          ⁢                                      2                                                                        ,                                    t                                                                    ]                                                                                            ·                                                                                                x                                  ⁡                                                                      [                                                                                                                  k                                        ⁢                                                                                                                                                                  ⁢                                        1                                                                            ,                                      t                                                                        ]                                                                                                  *                                                                                                              )                                                ·                                                  w                          ⁡                                                      [                                                          k                              ⁢                                                                                                                          ⁢                              1                                                        ]                                                                                              )                                                                                                                                              =                            ⁢                                                                    1                    2                                    ·                                      W                    H                                                  ⁢                AW                                                                        (        3        )            
In Expression (3), W is a weight vector, and is given by Expression (4):
                    [                  Math          .                                          ⁢          4                ]                                                            W        =                  [                                                                      w                  ⁡                                      [                    1                    ]                                                                                                                        w                  ⁡                                      [                    2                    ]                                                                                                      ⋮                                                                                      w                  ⁡                                      [                    n                    ]                                                                                ]                                    (        4        )            
A is a correlation matrix of an input signal, and is given by Expression (5):
                                              ⁢                  [                      Math            .                                                  ⁢            5                    ]                                                                    A        =                              ∑            t                    ⁢                      [                                                                                                      x                      ⁡                                              [                                                  1                          ,                          t                                                ]                                                              ·                                                                  x                        ⁡                                                  [                                                      1                            ,                            t                                                    ]                                                                    *                                                                                                                                  x                      ⁡                                              [                                                  1                          ,                          t                                                ]                                                              ·                                                                  x                        ⁡                                                  [                                                      2                            ,                            t                                                    ]                                                                    *                                                                                        …                                                                                            x                      ⁡                                              [                                                  1                          ,                          t                                                ]                                                              ·                                                                  x                        ⁡                                                  [                                                      n                            ,                            t                                                    ]                                                                    *                                                                                                                                                              x                      ⁡                                              [                                                  2                          ,                          t                                                ]                                                              ·                                                                  x                        ⁡                                                  [                                                      1                            ,                            t                                                    ]                                                                    *                                                                                                                                  x                      ⁡                                              [                                                  2                          ,                          t                                                ]                                                              ·                                                                  x                        ⁡                                                  [                                                      2                            ,                            t                                                    ]                                                                    *                                                                                        …                                                                                            x                      ⁡                                              [                                                  2                          ,                          t                                                ]                                                              ·                                                                  x                        ⁡                                                  [                                                      n                            ,                            t                                                    ]                                                                    *                                                                                                                    ⋮                                                  ⋮                                                  ⋱                                                  ⋮                                                                                                                        x                      ⁡                                              [                                                  n                          ,                          t                                                ]                                                              ·                                                                  x                        ⁡                                                  [                                                      1                            ,                            t                                                    ]                                                                    *                                                                                                                                  x                      ⁡                                              [                                                  n                          ,                          t                                                ]                                                              ·                                                                  x                        ⁡                                                  [                                                      2                            ,                            t                                                    ]                                                                    *                                                                                        …                                                                                            x                      ⁡                                              [                                                  n                          ,                          t                                                ]                                                              ·                                                                  x                        ⁡                                                  [                                                      n                            ,                            t                                                    ]                                                                    *                                                                                            ]                                              (        5        )            
On the other hand, it is known that the constraint of the CMP method, that the signal gain from a desired direction is constant, can be given by Expression (6) using a constraint vector C which corresponds to the desired direction:[Math. 6]CHW=1  (6)
Here the superscript “H” on the right shoulder of the variable identifies the complex conjugate of the transpose of the matrix. Therefore if a weight vector Wmin, which minimizes the received power P in Expression (3), is calculated using Expression (6) as the constraint, and the calculated weight vector Wmin is substituted into Expression (1), then a received signal of the array antenna based on the CMP method can be calculated. In actual calculation, the weight vector Wmin is obtained as Expression (7):
                    [                  Math          .                                          ⁢          7                ]                                                                      W                      m            ⁢                                                  ⁢            i            ⁢                                                  ⁢            n                          =                                            A                              -                1                                      ⁢            C                                              C              H                        ⁢                          A                              -                1                                      ⁢            C                                              (        7        )            
The minimum received power Pmin is obtained as Expression (8):
                    [                  Math          .                                          ⁢          8                ]                                                                      P                      m            ⁢                                                  ⁢            i            ⁢                                                  ⁢            n                          =                  1                                    C              H                        ⁢                          A                              -                1                                      ⁢            C                                              (        8        )            
In other words, to calculate a received signal of the array antenna using the CMP method, the following [1] to [3] are sequentially executed:
[1] The correlation matrix A of Expression (5) is calculated using the input signal x[k, t].
[2] The weight coefficient vector Wmin in Expression (7) is calculated using the constraint vector C and the correlation matrix A.
[3] The received signal in Expression (2) is calculated using the weight coefficient vector Wmin and the input signal x[k, t].
If only the power of the received signals is required as a received signal, the minimum power Pmin calculated by Expression (8) is simply used as the received signal. Then a signal having a good SN ratio is obtained with minimum influence of any interfering waves.
Non-patent Literature 1 (NPL 1) reports an example of applying the CMP method to ultrasound echo image processing. The ultrasound echo image processing is processing for generating an image of a structure inside an object by irradiating an object with an ultrasound beam, and receiving ultrasound waves reflected inside the object by a plurality of receiving elements arrayed one-dimensionally or two-dimensionally. If a probe constituted by the plurality of receiving elements is regarded as an array antenna and the CMP method is applied to the processing of received signals, then an improvement in performance of the ultrasound echo image processing can be expected.